Forecasting real estate returns using financial spreads

Article

Accepted Version

Brooks, C. and Tsolacos, S. (2001) Forecasting real estate returns using financial spreads. Journal of Property Research, 18 (3). pp. 235-248. ISSN 1466-4453 doi: https://doi.org/10.1080/09599910110060037 Available at http://centaur.reading.ac.uk/35970/

It is advisable to refer to the publisher’s version if you intend to cite from the work. See Guidance on citing .Published version at: http://dx.doi.org/10.1080/09599910110060037

To link to this article DOI: http://dx.doi.org/10.1080/09599910110060037

Publisher: Routledge

All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement .

www.reading.ac.uk/centaur

CentAUR

Central Archive at the University of Reading

Reading’s research outputs online

This is an Author's Accepted Manuscript of an article published in the

Journal of Property Research (2001) [copyright Taylor & Francis],

available online at: www.tandfonline.com/10.1080/09599910110060037

2

Forecasting Real Estate Returns using Financial Spreads

Chris Brooks (corresponding author), ISMA Centre, PO Box 242, The University of

Reading, Whiteknights, Reading RG6 6BA; e-mail: C.Brooks@reading.ac.uk

and

Sotiris Tsolacos, Jones Lang LaSalle, 22 Hanover Square, London, W1A 2BN

October 2000

Forecasting Real Estate Returns using Financial Spreads

Abstract

This paper examines the predictability of real estate asset returns using a number of time

series techniques. A vector autoregressive model, which incorporates financial spreads, is

able to improve upon the out of sample forecasting performance of univariate time series

models at a short forecasting horizon. However, as the forecasting horizon increases, the

explanatory power of such models is reduced, so that returns on real estate assets are best

forecast using the long term mean of the series. In the case of indirect property returns,

such short-term forecasts can be turned into a trading rule that can generate excess returns

over a buy-and-hold strategy gross of transactions costs, although none of the trading

rules we develop could cover the associated transactions costs. We therefore conclude

that such forecastability is entirely consistent with stock market efficiency.

J.E.L. Classifications: C32, C52

Keywords: real estate returns, spreads, forecasting, time series models, vector

autoregressions

The authors acknowledge comments from two anonymous referees on a previous version of the paper.

The usual disclaimer applies.

1

1. Introduction

There is considerable evidence in the real estate literature that the behaviour of real estate

returns, that is returns on real estate-backed assets, are related to economic trends and

changing business conditions, and that they can be modelled, at least in part, using

publicly available economic information (Chan et al, 1990; McCue and Kling, 1994 and

Ling and Naranjo, 1997). This information is contained in a number of well publicised

macroeconomic financial time-series used in financial markets. Two variables commonly

used in the existing literature as indicators of future economic and monetary conditions

are the term structure of interest rates and the gilt-equity ratio. Research in the area of real

estate return predictability has been extended to investigate the possibility of superior

investment performance of real estate portfolios utilising the predictive power of real

economy variables and of financial aggregates.

Since the large majority of these studies examine the predictability of real estate returns

in the context of the US, further research is warranted to provide empirical evidence on

the linkages between the macroeconomy and real estate returns in other markets. This

need is particularly pronounced in European markets where equity investors are

increasingly considering real estate backed stocks as an investment vehicle in their

portfolios (see Ball et al (1998) for the increasing importance of the indirect property

vehicles). Although all equities are valued according to the expected future profit stream

of the firms, it can be argued that the fundamentals underpinning these profit streams and

returns on real estate backed stocks may differ from those on other types of stocks,

resulting in distinct time series behaviour of returns between these asset classes. The

main reason for this feature is the fact that the former are expected to reflect conditions in

the underlying direct property market. This, coupled with the evidence that real estate

2

returns seem to be more predictable than returns on other assets (Liu and Mei, 1992),

makes it possible that investors might be able to exploit this predictability in order to

pursue more profitable investment strategies, or more efficient portfolio diversification in

the mean-variance sense than portfolios which exclude real estate as an asset class. In

addition, although previous studies have explained the historical variation in real estate

returns using a set of predetermined variables within pre-specified frameworks, such as

multifactor regression models and vector autoregressions, they have not tested for the

forecasting ability of the different methodologies and variables. Therefore, the question

that arises is how accurately the real estate return generating models in the existing

literature predict the direction in future values of real estate returns and how suitable they

are for the purpose of short-term and longer term forecasting.

The main thrust of the present study is to examine the performance of alternative

econometric methodologies in forecasting real estate returns in the short-run in the UK.

Real estate returns are defined as the growth rate in the Primark Datastream price index

of real estate stocks. An analyst can study the time series properties of past data on real

estate returns and utilise this information to make short term predictions. Alternatively,

these forecasts can be made based upon a more general modelling methodology of real

estate return determination which includes information contained in lagged

macroeconomic or financial variables. The particular aim of this research is to forecast

the short- and long-run variation in real estate returns utilising both the time series

properties of the returns series alone and then a multivariate model that incorporates the

term structure of interest rates and the gilt-equity yield ratio to exploit the economic

information content of these variables. It is very important that investors have evidence

on whether the time series properties of real estate returns can be used for forecasting

3

purposes or whether they should employ more general models and frameworks to carry

out the forecasting analysis. This study provides the first evidence on comparative

forecasting research work in the field of real estate returns in the UK based on four

different prediction methodologies. The study also evaluates whether the relative

forecasting accuracy of these methodologies is invariant as the forecasting horizon

becomes longer.

The remainder of the paper is organised in five sections. A discussion of the methodology

followed and data employed in this paper is presented in section 2. Section 3 reports the

empirical findings while section 4 presents a comparative analysis of the forecastability

of direct and indirect property returns. Section 5 offers a trading rule to exploit potential

forecastabilities in the indirect returns series, and finally, section 6 concludes.

2. Forecasting frameworks, data, and production of forecasts

The simplest approach to forecasting real estate returns is to utilise the time series

properties of the returns series itself. For this purpose, forecasts are derived from two

models: (i) a forecasting model that simply comprises the long term mean of the returns

series, estimated as the unconditional mean of a trailing sample (in this case of size 200

observations) and (ii) an ARMA model which is fitted to the property returns series, with

the optimal model order being chosen by Akaike’s information criterion, Schwarz’s

Bayesian criterion, and the Hannan-Quinn criterion.

An third approach to forecasting real estate returns is to consider additional explanatory

variables that explicitly incorporate analysts’ expectations about business conditions in a

vector autoregressive (VAR) model framework. The set of variables for inclusion in the

4

VAR is determined by the conclusions of recent research investigating the modelling of

stock returns or real estate returns. It is assumed that changing economic conditions are

ultimately responsible for the variation in property share prices. There is ample evidence

in applied economics research that the term structure of interest rates and the gilt-equity

yield ratio (GEYR) adjust when market participants revise their expectations about the

state of the economy. Therefore, they can be used as leading indicators of future business

conditions (Estrella and Hardouvelis, 1991; Hardouvelis, 1994; Davis and Fagan, 1997).

Several authors have argued that the term structure of interest rates contains information

about the future course of the economy (Campbell, 1987; Chen, 1991; Estrella and

Hardouvelis, 1991; Hardouvelis, 1994). In particular, Estrella and Hardouvelis (1991)

demonstrate that the yield curve has predictive power beyond that contained in the short

term interest rate, and can help predict changes in national output up to four periods

ahead. The term structure of interest rates is defined as the difference between the long-

term and the short-term rates of interest. This spread is usually positive so that the yield

curve is upward sloping. A tightening of monetary policy in order to kerb inflation or

inflationary growth will be reflected in higher short-term interest rates. If the financial

markets believe that future economic activity will slow down and therefore that the future

short-term rate of interest will fall, the yield curve will flatten out or even decline. High

short rates in the current period can lead to lower aggregate investment expenditure that

in turn results in a decline in future economic activity. Therefore, market participants

expect lower prices and returns on traded property assets during the forthcoming

economic contraction. Chan et al (1992) provide supporting evidence to the view that the

term structure affects real estate returns but Liu and Mei (1992) did not find such

5

evidence. On the other hand, Ling and Naranjo (1997) found that the spread variable

could become important in particular periods.

The predictive power of the gilt-equity yield ratio has not been examined in the literature

on real estate returns, although research on general equity market indices suggests that it

can have additional explanatory power beyond that contained in other macroeconomic or

financial variables (see Levin & Wright, 1999; Brooks and Persand, 2000). The GEYR

ratio is measured as the ratio of the long gilt yield to the equity dividend yield. Levin and

Wright argue that the GEYR has a normal “long run” level, reflecting a long run no-

arbitrage relation between government bond and equity markets. Movements in this ratio

are strongly affected by changes in the stock price and dividend yield (see Davis and

Fagan, 1997). If, due to higher expected profitability, the dividend yield falls, the GEYR

may become too high so that equities are thought expensive relative to bonds. Levin and

Wright also state that bond yields do not fall, the low value of equity yields cannot be

sustained. Therefore, equity prices, and in the context of the present study, the prices of

property stocks, must fall to restore the long run equilibrium. When the GEYR is too low,

equity prices are expected to rise in order to restore the equilibrium relationship.

Other macroeconomic variables, such as changes in unemployment, inflation, short term

interest rates are not included in the results given here for two reasons. First, the results

obtained by using these variables (not reported but available from the authors upon

request) were inferior to those reported here using the two financial variables. Second,

recent research by Brooks and Tsolacos (1999) has shown that the other variables do not

even have any in-sample predictive power for real estate returns, evidenced by the joint

6

lack of significance of the coefficients in the VAR representations when general stock

market effects are removed.

The data employed in this study comprise monthly observations on the Primark

Datastream UK Property Index, the term spread (measured as the difference between the

yields on a 20 year government bond and the three month Treasury bill rate), and the gilt-

equity yield ratio (calculated by taking the ratio of the yield on 20 year government bonds

and the dividend yield on the FTSE 100). All data were obtained from Datastream

International, and cover the period January 1968 until January 1998, yielding a total of

361 sample points. The property index employed comprises a market value-weighted

index constructed by Primark Datastream, based upon the top 26 property stocks traded

on the London Stock Exchange. The relative weightings given to the component stocks

are updated on a monthly basis.

Some summary statistics for the data are presented in table 1. The property returns series

shows significant autocorrelation at the first lag, but none thereafter, and is both skewed

and leptokurtic. Meanwhile, the GEYR series is leptokurtic but not skewed, and the

spread series seems to show little departure from normality. Both the GEYR and spread

series are very strongly autocorrelated, but there is no evidence that any of the series are

non-stationary.

The effect of the above variables is examined within the context of an unrestricted

reduced-form vector autoregressive (VAR) model, with three equations (one for each of

the three variables: real estate returns, the term structure, GEYR), which is described by:

Yt = 0 + 1Yt-1 + ... + mYt-m + ut (1)

7

where Y is the set (or 31 vector) of variables included in the system, the terms give the

sets of coefficient vectors (0 is a 31 vector of constants, 1 ,..., m are 33 matrices of

coefficients on the lagged variables, m represents the number of lags of each variable in

each equation), and ut is a vector of error terms (or innovations) which are assumed to be

mutually uncorrelated and independent of the Ys. The number of lags of each variable to

be included in the VAR is chosen using multivariate generalisations of Akaike’s

Schwarz’s Bayesian, and the Hannan-Quinn information criterion (see, for example,

Enders, 1995).

The forecasts are constructed as follows. The sample is split roughly in half, with the first

200 observations being used for in-sample model estimation. Then a series of out of

sample forecasts up to six steps ahead are generated. The sample is then rolled forward

by one observation, the models re-estimated, and a new series of forecasts constructed.

This procedure is repeated until 160 such forecasts are generated. The UK economy has

been the subject of numerous changes in monetary and fiscal policy over our 30 year

sample period (see below), and thus the use of shorter windows used in a rolling fashion

helps to minimise the possibilities of structural breaks whilst ensuring sufficient in-

sample data to estimate the models and to produce the forecasts.

The forecasts for the different models are evaluated and compared on the grounds of

mean squared error (MSE), mean absolute error (MAE) and the proportion of times that

the model correctly predicts the return’s sign. The “best” model is defined as the one with

the lowest mean squared or mean absolute error, since this would indicate the model

whose forecasts are closer to the realised values of the series, and whose forecasts are

therefore the most accurate. However, it has also been shown (Gerlow et al., 1993) that

8

the accuracy of forecasts according to traditional statistical criteria may give little guide

to the potential profitability of employing those forecasts in a market trading strategy, so

that models which perform poorly on statistical grounds may still yield a profit if used for

trading, and vice-versa. Models that can accurately forecast the sign of future returns, or

can predict turning points in a series have been found to be more profitable (Leitch and

Tanner, 1991). Hence the proportion of times that the model correctly predicts the sign of

the real estate return is also calculated.

In table 2, we present the results of Granger-causality tests for the three variables

employed in the analysis, used to determine whether the VAR formulation seems sensible

or not. A detailed description of the operation of this test and its interpretation can be

found in Brooks and Tsolacos (1999). Changes in the property index are found to be

caused by previous changes in its own values, and by previous changes in the values of

the GEYR and the interest rate spread. Meanwhile, changes in the property index do not

seem to Granger-cause changes in either of the other two series. Thus we conclude that

the other two variables are weakly exogenous, and that the additional information

contained in the GEYR and the term spread could be useful for modelling and forecasting

changes in the property index.

3. Results

Initially the order of the ARMA and the VAR models was established as accomplished

by the three information criteria. The in-sample minimisation of Akaike’s criterion

suggested that four lags of the autoregressive part and two lags of the moving average

term should be used, while the other two criteria both favoured an ARMA(1,1) model.

For the VAR model the same criteria indicated the inclusion of four lags, one lag and one

9

lag respectively. We employ the same number of lags for each variable so that the VAR

is completely unrestricted. The results for the out of sample forecasts generated using the

different methods, with ARMA and VAR models being estimated using the numbers of

lags suggested by all the criteria, are given in Table 3 for 1 and 6 month prediction

horizons.

In this application, the forecast accuracy evaluation measures give differing orderings of

models. The VAR models, which attempt to incorporate the macroeconomic influences

of the term spread and the gilt-equity yield ratio, give surprisingly poor overall

performances for a forecasting horizon of one or six steps ahead, on MSE or MAE

grounds. When evaluated using these criteria, the VAR(4) does particularly badly, and

presumably represents an over-parameterisation, given that there are 12 right-hand side

variables plus a constant, in each equation. The VAR(1), on the other hand, whilst not the

best model, produces 1-step ahead forecasts which are among the most accurate. Even the

small VAR model rapidly loses forecasting power, however, as the forecast horizon is

extended. This is not surprising, since to produce multi-step ahead forecasts from a VAR,

the values of the other variables in the system must also be forecasted (within the

system), which introduces another source of uncertainty and potential error. In order to

further evaluate why the VAR model (which contains all of the information in the

univariate autoregressive framework, plus additional variables) did not produce superior

forecasts compared with simpler models, we compute and plot in Figures 1 to 3 the

impulse-response functions associated with unit shocks in each of the three explanatory

variables, which are subsequently tracked for 24 months. Considering the signs of the

responses, changes in the value of the property index are positively correlated over a

short horizon, since the impulse response is large positive for lags 1 and 2, but the

10

impulse-responses thereafter are negative, although the two standard error bands (the

dotted lines) span the horizontal axis, indicating that the impulse-response coefficients

are no longer significant. The response of the property index to changes in the GEYR, in

Figure 2, shows no clear pattern over time. The unit shock of GEYR leads first to a rise,

then a fall, and then a rise in the value of the property index, although overall the effect is

positive. Similarly for changes in the term spread, the effect upon the real estate index is

difficult to determine, with first a fall, and then a rise, and then a fall in the value of the

index following a unit shock. For all three plots, however, it is clear that after perhaps 5

or 6 periods, the effects of the shocks for the current value of the property index returns,

are negligible.

The best models, for short-term forecasts are the long term mean on MSE grounds, and

the profligate ARMA(4,2) on MAE grounds, while the VAR(4) produces the highest

proportion of correct sign predictions. For the 6-month ahead forecasts, the long term

mean produces the most accurate forecasts under all evaluation measures.

4. The Forecastability of Direct Versus Indirect Property Investment Returns

In this section, we compare the relative forecast accuracies of the various models

presented above using the returns on both the indirect property investment vehicle (the

equity quoted property index) and the returns on a direct property investment index - the

IPD monthly total return series. The latter is compiled from valuation and management

records for individual buildings in complete portfolios. The IPD total return is defined as

the overall return on capital employed and is the sum of income return and capital

growth. The Income return is income receivable net of management and irrecoverable

costs divided by capital employed through the month. Capital growth is the change in

11

capital value from one valuation to the next, net of any capital flows, divided by capital

employed (more information can be found in the IPD UK monthly index publications).

Since the IPD series is only available from December 1986, we also re-compute the

forecasts for the indirect property series analysed above for the same sample periods in

order to facilitate comparisons. Thus forecasts are now generated using a moving window

of 5 years’ (60 months’) worth of data, with forecasts up to 6 steps ahead being generated

and then the sample rolled forward 1 observation until 74 such forecasts are produced.

The results are presented in tables 4 and 5.

Again, model orders are chosen using Akaike’s, Schwarz’s Bayesian, and the Hannan-

Quinn information criteria. These criteria chose for indirect property series, and for the

ARMA models, a (2,5) - all criteria; for the direct (IPD) series the selected models were

(6,3) - AIC, (3,4) - SBIC and HQIC. All three criteria chose a VAR(1) for the indirect

series, while AIC chose a VAR(2), but SBIC and HQIC chose a VAR(1) for the direct

series. The fact that the selected lag-lengths and sizes of models are larger for the direct

property returns is indicative that there is potentially more forecastable structure in this

series than that based on equities.

The results in table 4 are broadly similar to those in table 3, although there are some

differences due to the change in sample length and the timing of the estimation and

forecasts. In table 4, the VAR model for the indirect returns is almost universally

superior. It provides the lowest MSE and MAE, and the highest proportion of correct sign

predictions, except at the longest forecasting horizon, where the VAR is the worst model

for sign prediction, getting only half of the 6-step ahead signs right.

12

Table 5 presents the results for the appraisal-based IPD series. In this case, it is clearly the

ARMA approach, based upon only lags of the property returns themselves, which is the

winner, while the VAR model, containing additional information regarding the financial

markets, provides the least accurate forecasts, except in terms of sign predictions. The

parsimonious VAR(1) model provides a marginally higher proportion of correct sign

predictions at the short forecasting horizon, although the ARMA(1,1) and ARMA(1,3)

models are better as the prediction horizon increases.

In general, we can state that the use of “generous” information criteria, such as Akaike’s,

will lead to the selection of models which are over-parameterised, leading to poor

forecasts. Those concerned with forecasting real estate returns should be concerned to use

small models which do not use up valuable degrees of freedom, and which can

generalise.

It seems also that there is a great deal more forecastability in the appraisal-based, as

opposed to the equity-based series. This is evidenced by the fact that some models are

able to correctly predict the direction of change of the former series up to 6 months ahead

with over 90% accuracy. In financial markets, this accuracy would be considered

phenomenal. The mean absolute and mean squared errors of the time series and VAR

models are still smaller than those based on the long term mean, even at the 6 months

ahead horizon. This is, however, hardly surprising, and the apparent predictability of the

direct returns could be merely a statistical artefact, resulting from appraiser-induced

smoothness of the series. This smoothness in the series is exacerbated by the frequency of

the valuations. Monthly valuations of commercial properties do not provide sufficient

time for economic and other information to induce a significant variation in total returns.

13

Therefore, current returns are bound to be linked to previous returns since they are not

traded at the frequency of the property shares. On the other hand, this long memory in

direct property returns may reflect characteristics of the property market that result in

cyclical shocks having long-term effects on rental and capital values.

4. Production and testing of trading rules

Although the evidence for the apparent predictability of property returns, both direct and

indirect, may be considered prima facie evidence of stock market informational

inefficiency. However, according to modern definitions of stock market efficiency, a

market may only be considered inefficient with respect to a particular information set if it

is possible to make abnormal profits from trading on the basis of that information set. In

order to investigate whether we can find any evidence of property market informational

inefficiency, we develop a set of trading rules based on the forecasts produced as

discussed above. For the reasons outlined above, the trading rules are developed only in

the context of indirect, equity-based property returns. The results of a trading rule based

on appraisal-based returns are likely to be misleading and unrealistic since such returns

are not based on transactions data, and therefore it may not in fact have been possible to

buy or sell property at the prevailing valuation prices. Additionally, investing in direct

property is likely to occur large transactions costs and market orders to buy or sell direct

property will only be executed with a long lag.

Although there are an infinite number of ways to operationalise a trading rule, we

consider a simple approach where an investor is either long the equity-based property

index or has no position, with the funds being held in treasury bills and therefore earning

the short term “risk-free” rate of interest. The 1-step and 6-step ahead forecasts are

14

produced, and a decision about whether to be in property is made on that basis. We

employ two rules: first, invest in the property stock index if the property return during the

next period is forecast to be positive; second, invest in property only if the return forecast

for the next month is greater than the average return over the sample period (i.e. greater

than 0.87% per month). In each case, if a return is predicted to be sufficiently large to

signal a buy, the property index notionally purchased. Then, the sample is rolled forward

one observation, and if the next return predicted positive again, the index continues to be

held, and so on. If the return is then predicted to be negative, however, the index is sold,

with the proceeds invested in the risk free rate. It is assumed that the investment began at

the start of our out of sample period and continued for the full 160 observations (i.e. a 13

years and 4 month period). We can effectively ignore risk in these calculations, since the

benchmark will be a “buy-and-hold the property index” approach, and this is likely to

represent more risk than our trading strategies, which involve being out of equities and in

treasury bills for part of the period.

Table 6 presents the trading profitability results, denominated in simple annualised

percentage returns, for each of the 5 models. The long-term mean model produces

property return forecasts that are always (small and) positive. Therefore, the long term

mean rule would be identical to passively holding the property index throughout the

whole period. The simple average annualised return to simply holding the property index

throughout is 8.07%. Overall, some of the models are able to modestly improve on this

profitability. The best performing models in aggregate are the VAR models, which

produce returns in excess of 9% per annum for the 1 step ahead forecasts with holdings in

equities being based on any positive forecasted returns. In general, as one might have

anticipated, trading on the basis of the 1-step ahead forecasts is more profitable than

15

trading on the basis of the 6-step ahead forecasts. Such a result ties in with the statistical

evaluation, which showed that the one step ahead forecasts are typically more accurate

and give a higher percentage of correct sign predictions.

A further cautionary note is required, however, in interpreting these results. The returns

presented in table 6 are calculated gross of transactions costs. Sutcliffe (1997) suggests

that an appropriate “round-trip” figure for transacting in companies contained in the

FTSE-100 is 1.7% of the value of the purchase/sale per transaction for an investor. This

figure is made up of bid /ask spread (0.8%), stamp duty (0.5%) and commission (0.4%).

Even ignoring the fact that some of the companies in the property index are not in the

FTSE 100, and are therefore likely to be less liquid with higher spreads, these

transactions costs are likely to wipe out any profits made by the trading rules. The best

performing rule generates a return of 9.26% per annum, but would generate

approximately 3-4 trades per year, resulting in transactions costs of around 6% per

annum. A filter which states that investors should only buy into the property index when

the index is predicted to rise by more than its historical average, typically results in fewer

trades, but also generates lower gross returns. For example, the best performing model in

the context of the strict filter is the VAR(1) using one-step ahead predictions, giving an

average annual return of 8.70%. This rule still requires 37 trades over the out of sample

period (approximately 2-3 trades per year), again wiping out any excess gross

profitability over a pure buy-and-hold equities strategy. Under modern definitions of

market efficiency, forecastability in returns can only be considered evidence for market

informational inefficiency if those forecasts can be turned into a trading rule that

generates abnormal returns net of costs. Since our trading rules could not generate excess

returns net of transactions costs, we would infer that the apparent forecastability of

16

indirect property returns is entirely consistent with stock market efficiency and the

absence of possibilities for arbitrage.

6. Conclusions

The present study examined the performance of three different forecasting techniques that

are available to analysts and investors to forecast real estate returns in the UK. Two of

these techniques utilise the time-series properties of the real estate return series. The third

methodology is a VAR model that allows the testing of the role of the term structure of

interest rates and the gilt-equity yield ratio in forecasting real estate returns. Forecasts

were produced for one to six months ahead and evaluated on the basis of standard

forecast evaluation criteria.

This investigation has found that a vector autoregressive model, incorporating lagged

values of term structure of interest rates and the gilt-equity yield ratio, provides superior

one step (month) ahead predictions of real estate returns than other simpler univariate and

naive forecasting models. However, at longer predictive horizons (that is up to six

months), the relative advantage of the more complex multivariate model for forecasting

equity-based returns disappears. The implication of this finding is that the multivariate

asset pricing models developed in existing work to explain the intertemporal variation in

real estate returns may only be suitable for immediate or short-term forecasts (one to two

steps ahead). The recommendation in the present paper is that analysts can do no better

than to forecast the long term behaviour of indirect, equity-based real estate returns series

based on its long term mean. The short run variation around the mean can be forecast

using multi-factor frameworks. Meanwhile, returns to direct property investments appear

prima facie to be forecastable using time series models at least 6 periods into the future.

17

In the case of indirect property returns, such short-term forecasts can be turned into a

trading rule that can generate excess returns over a buy-and-hold strategy gross of

transactions costs, although none of the trading rules we develop could cover the

associated transactions costs. We therefore conclude that such forecastability is entirely

consistent with stock market efficiency.

18

References

Akaike, H.(1974) A New Look at the Statistical Model Identification IEEE Transactions on

Automatic Control AC-19(6), 716-723

Ball, M., Lizieri, C. and MacGregor, B. (1998) The Economics of Commercial Property Markets,

Routledge, London.

Brooks, C. and Persand, G. (2000) The Trading Profitability of Forecasts of the Gilt-Equity

Yield Ratio International Journal of Forecasting forthcoming

Brooks, C. and Tsolacos, T. (1999) The Impact of Economic and Financial Factors on UK

Property Performance Journal of Property Research 16(2), 139-152

Chan, K.C., Hendershott, P.H. and Sanders, A.B. (1990) Risk and return on real estate: evidence

from equity REITs, American Real Estate and Urban Economics Association Journal 18, 431-

52.

Davis, E.P. and Fagan, G. (1997) Are Financial Spreads Useful Indicators of Future Inflation and

Output Growth in EU Countries? Journal of Applied Econometrics 12, 701-714.

Enders, W.A. (1995) Applied Econometric Time Series Wiley, New York.

Estrella, A. and Hardouvelis, G.A. (1991) The Term Structure as a Predictor of Real Economic

Activity. Journal of Finance 46, 555-576

Gerlow, M.E., Irwin, S.H. and Liu, T-R. (1993) Economic Evaluation of Commodity Price

Forecasting Models International Journal of Forecasting 9, 387-397

Hardouvelis, G. (1994) The term structure spread and future changes in long and short rates in

the G7 countries, Journal of Monetary Economics 33, 255-83.

Leitch, G. and Tanner, J.E., (1991) Economic Forecast Evaluation: Profit Versus the

Conventional Error Measures American Economic Review 81(3), 580-590

Levin E.J. and Wright, R.E., (1998) The Information Content of the Gilt-Equity Yield Ratio

Manchester School Supplement, 89-101

Ling, D. and Naranjo, A. (1997) Economic risk factors and commercial real estate returns,

Journal of Real Estate Finance and Economics 14, 283-307.

Liu, C.H. and Mei, J. (1992) The predictability of returns on equity REITs and their co-

movement with other assets, Journal of Real Estate Finance and Economics 5, 401-18.

McCue, T.E. and Kling, J.L. (1994) Real estate returns and the macroeconomy: some empirical

evidence from real estate investment trust data, 1972-1991, Journal of Real Estate Research

9(3), 5-32.

Sutcliffe, S. (1997) Stock Index Futures: Theories and International Evidence, Second Edition,

Thomson Business Press, London.

19

Table 1. Summary Statistics for the Variables 1968-1998

Statistic Indirect Property

Returns

Log-Changes in the

GEYR

Log-Term Spread

Mean 0.869 -0.814 1.182

Variance 64.720 0.015 5.000

Skewness -0.659** -0.061 -0.233

Excess Kurtosis 5.048** 1.174** 0.0346

Minimum -43.905 -1.199 -4.820

Maximum 38.869 -0.3512 6.730

Bera-Jarque 408.226** 20.909** 3.280

Acf(1) 0.125** 0.873** 0.960**

Acf(2) -0.099 0.752** 0.923**

Acf(3) -0.027 0.670** 0.883**

Acf(4) -0.022 0.562** 0.845**

Acf(5) -0.071 0.479** 0.810**

LB-Q*(12) 11.957 1063.998 1650.394**

Notes: Bera-Jarque is a normality test statistic, asymptotically distributed as a 2(2) under the null; Acf(x)

denotes the autocorrelation coefficient at lag x; * and ** denote significance at the 5% and 1% levels

respectively; LB-Q*(12) denotes the Ljung-Box statistic for autocorrelation of order up to 12, which is

distributed asymptotically as a 2(12) under the null.

Table 2. Granger Causality Tests for VAR(4)

Causality from (independent variable)

Indirect Property Index GEYR Term Spread

Causality to Indirect Property Index 0.0232 0.0193 0.0957

(Dependent GEYR 0.4954 0.0000 0.2978

Variable) Term Spread 0.5144 0.1154 0.0000

Note: Cell entries are p-values.

20

Table 3. Out of sample forecast accuracies for indirect (DS) property return

forecasting models 1968 - 1998

Steps Forecasts using

Long term mean ARMA(4,2) ARMA(1,1) ARMA(1,3) VAR(1) VAR(4)

Panel A: Mean Square Error

1 98.9625 143.8746 100.6335 100.7223 99.6245 114.0778

6 98.8341 153.9693 100.8244 100.6871 102.4357 109.0905

Panel B: Mean Absolute Error

1 7.2197 7.1819 7.3820 7.3307 7.2049 7.5951

6 7.2197 7.8485 7.3590 7.3500 7.3528 7.3528

Panel C: % Correct sign predictions

1 58.09 51.86 55.62 57.50 56.88 58.25

6 58.13 46.88 50.00 48.13 55.62 52.50

Table 4. Out of sample forecast accuracies for indirect (DS) property return

forecasting models 1986-1998

Steps Forecasts using

Long term mean ARMA(2,5) VAR(1)

Panel A: Mean Square Error

1 56.8638 76.0518 55.5625

6 56.8842 72.9506 46.4988

Panel B: Mean Absolute Error

1 5.8497 6.9969 5.7702

6 5.8521 6.6779 5.5091

Panel C: % Correct sign predictions

1 58.11 51.35 59.46

6 58.11 51.35 50.00

21

Table 5. Out of sample forecast accuracies for direct (IPD) property return

forecasting models 1986-1998

Steps Forecasts using

Long term

mean

ARMA(4,2) ARMA(1,1) ARMA(1,3) VAR(1) VAR(2)

Panel A: Mean Square Error

1 0.6717 0.2381 0.1729 0.1756 0.7052 0.7061

6 0.6724 0.8661 0.2668 0.2739 0.8917 0.9332

Panel B: Mean Absolute Error

1 0.5459 0.3598 0.2808 0.2999 0.6338 0.6527

6 0.5456 0.6212 0.3556 0.1766 0.7447 0.7677

Panel C: % Correct sign predictions

1 93.24 87.84 91.89 90.54 94.60 91.89

6 91.89 75.68 91.89 90.54 89.49 85.14

Table 6: Profitability of Indirect Property Index Trading Rules based on Out of

Sample Forecasts

Steps ahead

forecasts produced

for:

Trade when forecast next

return > 0.87% per month

Trade when forecast next return

positive

Number of

trades

Average

annual return

Number of

trades

Average

annual return

ARMA(1,3)

1 step ahead 23 2.69% 74 7.91%

6 steps ahead 1 2.95% 68 6.19%

ARMA(1,1)

1 step ahead 22 4.13% 66 8.93%

6 steps ahead 1 2.50% 76 1.87%

ARMA(4,2)

1 step ahead 48 4.55% 77 7.48%

6 steps ahead 34 8.50% 79 5.18%

VAR(4)

1 step ahead 37 7.82% 50 9.26%

6 steps ahead 34 2.28% 51 4.99%

VAR(1)

1 step ahead 37 8.70% 41 9.11%

6 steps ahead 56 3.50% 41 4.93%

Buy and hold equities 1 8.07%

Buy and hold treasury bills 1 2.50%

22

Figure 1: Impulse Responses and Standard Error Bands for

Innovations in the Property Index

-2

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Steps Ahead

Figure 2: Impulse Responses and Standard Error Bands for

Innovations in the GEYR

-1.5

-1

-0.5

0

0.5

1

1.5

1 3 5 7 9

11

13

15

17

19

21

23

Steps Ahead

23

Figure 3: Impulse Responses and Standard Error Bands for

Innovations in the Term Spread

-1.5

-1

-0.5

0

0.5

1

1 2 3 4 5 6 7 8 9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Steps Ahead